Problem 6 Perform the indicated operation.... [FREE SOLUTION]

Chapter 7: Problem 6

Perform the indicated operation. Simplify, if possible. \(\frac{5}{x}+\frac{6}{x^{2}}\)

Short Answer

Expert verified

\( \frac{13}{a^{2}} \)

Step by step solution

Combine the fractions

Since the denominators of the fractions are the same, combine the fractions by adding the numerators. \( \frac{4}{a^{2}} + \frac{9}{a^{2}} = \frac{4 + 9}{a^{2}} \)

Add the numerators

Add the numerators together.\( 4 + 9 = 13 \)

Write the combined fraction

Now write the combined result.\( \frac{4 + 9}{a^{2}} = \frac{13}{a^{2}} \)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Comparing denominators

When adding fractions, it's important to first check if the denominators are the same. The denominator is the bottom part of a fraction. In our example, the denominators are both \(a^2\). Since they match, we can move to the next step. Remember, if the denominators are different, we need to find a common denominator before we can add the fractions.
To find a common denominator, we typically look for the least common multiple (LCM) of the different denominators.
This step is crucial because fractions must refer to the same unit to be combined properly.

Adding fractions

Once we've confirmed the denominators match, we can add the fractions. To do this, keep the same denominator and add the numerators. In our example, we add the numerators of \(\frac{4}{a^2}\) and \(\frac{9}{a^2}\): \[ \frac{4}{a^2} + \frac{9}{a^2} = \frac{4 + 9}{a^2} \]
Notice how the denominator \(a^2\) remains unchanged throughout this process. Adding fractions requires aligning them under a common denominator so that only the numerators change.

Combining numerators

Now that we have an equivalent fraction with a common denominator, we combine the numerators. Simply add the top numbers (numerators) together, while keeping the denominator the same. For our example, the addition looks like this: \[ 4 + 9 = 13 \] Combining the numerators gives us the final fraction: \[ \frac{4 + 9}{a^2} = \frac{13}{a^2} \]
Therefore, the simplified result of our initial problem \( \frac{4}{a^2} + \frac{9}{a^2} \) is \( \frac{13}{a^2} \). This final fraction tells us the combined value, maintaining the same denominator.

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91影视

Perform the indicated operation. Simplify, if possible. \(\frac{5}{x}+\frac{6}{x^{2}}\)

Short Answer

Step by step solution

Combine the fractions

Add the numerators

Write the combined fraction

Key Concepts

Comparing denominators

Adding fractions

Combining numerators

One App. One Place for Learning.

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